CN112859617B - iPI model-free adaptive global nonsingular rapid terminal sliding mode control method - Google Patents
iPI model-free adaptive global nonsingular rapid terminal sliding mode control method Download PDFInfo
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Abstract
The invention discloses an iPI model-free self-adaptive global nonsingular rapid terminal sliding mode control method, which comprises the steps of establishing a mathematical model of a hypersonic aircraft aerodynamic heat ground simulation system and a super-local model without model control according to an energy conservation law; carrying out unknown disturbance prediction on the hypersonic aircraft aerodynamic heat ground simulation system by using a nonlinear ESO observer; based on the global nonsingular fast terminal sliding mode surface weakening approach buffeting, low convergence speed and singularity; and defining an equivalent control rate and a self-adaptive approach law according to the sliding mode accessibility condition to obtain a sliding mode control rate and finish target tracking. According to the method, through the design of the overall nonsingular quick terminal sliding mode surface, the approach mode is removed, so that the buffeting phenomenon is reduced, the control speed on the sliding mode is accelerated, the controller does not have the singularity problem due to the limitation on the sliding mode surface condition, and the convergence stagnation problem is effectively solved by combining a self-adaptive method.
Description
Technical Field
The invention relates to the technical field of aerospace automation, in particular to an iPI model-free self-adaptive global nonsingular rapid terminal sliding mode control method.
Background
As a common mode for ground thermal test simulation, compared with a nickel-chromium rod, a carbon silicon rod and a graphite rod which are used as heating elements in a thermal radiation test, the quartz lamp heater has the characteristics of long service life, high thermal efficiency, high temperature rise speed, compact structure, strong controllability and the like, and is widely applied to a hypersonic aircraft aerodynamic heat ground simulation test. As a quartz lamp heater for simulating the thermal environment of an aircraft, the quartz lamp heater is required to have good stability, accuracy, rapidity and anti-interference capability, so that a control method needs to be designed to meet the requirements of the performance indexes.
Conventional control methods can track the quartz lamp heater output temperature, but require accurate quartz lamp heater model parameters. Due to the influence of external unknown disturbance and self internal uncertain items, the traditional model-based control mode cannot be applied to the quartz lamp heater. Therefore, a model-free control mode is provided to act on the quartz lamp heater, and the super-local model is a mode of model-free control, but is only suitable for a single-input single-output system and requires that a converted controlled object expression can only be of a first order or a second order. And (3) adopting a hyper-local model in model-free control and combining an ESO extended state observer to carry out linearization processing on the mathematical model of the whole single-input single-output quartz lamp heater, wherein all unknown disturbances including definite, uncertain, unknown and known disturbances are tracked by the ESO extended observer.
In addition, the traditional PID control has the advantages of simple structure and easy debugging, but the control precision is not high enough, the convergence speed is low, and the overshoot is large. The sliding mode control in the modern control theory is superior to the traditional PID control in response speed, anti-interference capability and control accuracy, and has low requirement on the accuracy of the model, so the sliding mode control is widely applied. The terminal sliding mode has the characteristic of traditional sliding mode control and can be converged in limited time. However, the terminal sliding mode also has two stages of approach and sliding, and the problems of jitter, convergence stagnation, singular control and the like of the approach stage exist.
Disclosure of Invention
This section is for the purpose of summarizing some aspects of embodiments of the invention and to briefly introduce some preferred embodiments. In this section, as well as in the abstract and the title of the invention of this application, simplifications or omissions may be made to avoid obscuring the purpose of the section, the abstract and the title, and such simplifications or omissions are not intended to limit the scope of the invention.
The present invention has been made in view of the above-mentioned conventional problems.
Therefore, the iPI model-free adaptive global nonsingular fast terminal sliding mode control method provided by the invention can solve the problems that the expected temperature cannot be tracked within a limited time and the buffeting phenomenon in the control process is weakened.
In order to solve the technical problems, the invention provides the following technical scheme: the method comprises the steps of establishing a mathematical model of a hypersonic aircraft aerodynamic heat ground simulation system and a super-local model without model control according to an energy conservation law; carrying out unknown disturbance prediction on the hypersonic aircraft aerodynamic heat ground simulation system by using a nonlinear ESO observer; based on the global nonsingular fast terminal sliding mode surface weakening approach buffeting, low convergence speed and singularity; and defining an equivalent control rate and a self-adaptive approach law according to the sliding mode accessibility condition to obtain a sliding mode control rate and finish target tracking.
The iPI model-free adaptive global nonsingular fast terminal sliding mode control method is a preferable scheme, wherein: the hypersonic aircraft pneumatic heat ground simulation system comprises a non-contact radiation heater, an electric power regulating device and a calorimetric sensor; establishing an input and output energy conservation equation according to the energy conservation law to obtain the current temperature T1And the conduction angle alpha of the triac, as follows,
wherein, the left side U of the equationIThe input voltage is the voltage at two ends of the power supply, R is the sum of the resistances of the non-contact radiation heater, alpha is the conduction angle of the bidirectional thyristor, and the right side of the equation is respectively used for internal energy consumed by the non-contact radiation heater and heat energy and heat transfer lost in the convection heat exchange processHeat energy lost in the conduction process, heat energy output by heat radiation effect, c, m, T1、T0A, epsilon and delta t are respectively the specific heat capacity, mass, current temperature, initial temperature, surface area, blackness coefficient and working time of the non-contact radiation heater, and beta, lambda, sigma and F are respectively the convection heat transfer coefficient, heat conduction coefficient, Stefin-Boltzmann constant and angle coefficient.
The iPI model-free adaptive global nonsingular fast terminal sliding mode control method is a preferable scheme, wherein: comprises that when the controlled object model is a single-input single-output system, the controlled object model is converted into the model-free control super-local model, as follows,
y(n)＝G+χu(t)
wherein, y(n)The method is expressed as an nth derivative of an output quantity y to time t, n is generally 1 or 2, u is expressed as an input quantity, G is expressed as a set of all unknown disturbances, the unknown disturbances include external disturbances and system internal nonlinear disturbances, and χ is expressed as a non-physical adjustable parameter.
The iPI model-free adaptive global nonsingular fast terminal sliding mode control method is a preferable scheme, wherein: according to the model-free control super-local model, dividing two sides of the input and output energy conservation equation by delta t and performing term shift to obtain a mathematical model of the hypersonic aircraft aerodynamic heat ground simulation system, as follows,
wherein the content of the first and second substances,
is T1The derivative with respect to the time at is,
alpha respectively corresponds to y in the model-free controlled super-local model(n)U; sin2 alpha gives periodic shock to the systemThe term containing sin2 alpha can be regarded as an input disturbance, A epsilon sigma FT1 4Can be seen as a higher order output disturbance of the system and thus
The sum of all disturbances, which can be seen as both input and output disturbances, corresponds to the G of the hyper-local model, which can be observed by an observer.
The iPI model-free adaptive global nonsingular fast terminal sliding mode control method is a preferable scheme, wherein: also comprises the following steps of (1) preparing,
T1＝x3,G＝x4
wherein x is3Is the actual value T of the output1，x4In order to achieve a complete disturbance G,
is x3The first order differential of the first order of the,
is x4First order differential of (a) gamma is x4First order differentiation of; and carrying out unknown disturbance prediction on the hypersonic aircraft aerodynamic heat ground simulation system, and establishing the nonlinear ESO observer, as follows,
e1＝z1-x3,e2＝z2-x4
β1＞0,β2＞0
wherein Z is1Is x3Estimated value of, Z2Is x4Is determined by the estimated value of (c),
is Z1The first order differential of the first order of the,
is Z2First order differential of (1), beta1And beta1Is the gain of the parameter adjustment and the gain,
the iPI model-free adaptive global nonsingular fast terminal sliding mode control method is a preferable scheme, wherein: further included, the tracking error expression defining the output is as follows,
e(t)＝y*-y
where e is the tracking error, y*Is an output target; obtaining a model-free controller through closed-loop control according to the model-free controlled super-local model, as follows,
wherein the content of the first and second substances,
is an estimate of the value of G,
is y*Is the first order differential of (d), delta (e) is the iPI closed loop feedback control rate, delta (e) ═ Kpe(t)+KiIntegral; in order to attenuate the observed disturbances, an auxiliary controller u is added to the modeless controllerauxThe following, as follows,
wherein u isauxIs controlled according to a global nonsingular fast terminal sliding mode.
The iPI model-free adaptive global nonsingular fast terminal sliding mode control method is a preferable scheme, wherein: establishing the global nonsingular fast terminal sliding mode surface, including,
η＞0,ι＞0
wherein eta and iota are adjustable gains, p and q are positive odd numbers, the inequality p < q < 2p is satisfied, e (0) is an initial error, and s (0) ═ 0 solves the problem of approaching buffeting, e (tau) + iota e (tau)p/qSolves the problems of slow convergence speed and singularity,
is the first differential of the slip-form surface s.
The iPI model-free adaptive global nonsingular fast terminal sliding mode control method is a preferable scheme, wherein: further comprising establishing a tracking error e and an auxiliary controller uauxThe mathematical relationship between them, as follows,
wherein the content of the first and second substances,
in order to observe the error, the error is observed,
gidisturbing an upper bound for the observation error; according to
Substituting the above formula into the global nonsingular fast terminal sliding mode surface to obtain the final productTo the equivalent control rate, as follows,
according to sliding mode accessibility
The obtained approach rate was as follows,
wherein, k is the adjustable gain,
in order to adaptively perturb the upper bound adaptation rate,
the iPI model-free adaptive global nonsingular fast terminal sliding mode control method is a preferable scheme, wherein: the method comprises the steps of simultaneously fusing the auxiliary controller, the equivalent controller and the approach rate to obtain an iPI model-free self-adaptive global nonsingular fast terminal sliding mode controller u (t) of the hypersonic aircraft aerodynamic thermal ground simulation system, wherein the following steps are included,
wherein u isaux＝ueq+ucor。
The invention has the beneficial effects that: the global nonsingular rapid terminal sliding mode control method is combined with a model-free control super-local model and applied to a hypersonic aircraft aerodynamic heat ground simulation system, a mathematical model of the hypersonic aircraft aerodynamic heat ground simulation system is subjected to linearization processing, and a nonlinear ESO observer is used for observing all unknown disturbances; meanwhile, the design of the overall nonsingular fast terminal sliding mode surface removes the approach mode, so that the whole control stage is carried out on the sliding mode, the buffeting phenomenon is reduced, the control speed on the sliding mode is accelerated, the controller does not have the singularity problem due to the limitation on the sliding mode surface condition, and the convergence stagnation problem is effectively solved by combining a self-adaptive method.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without inventive exercise. Wherein:
fig. 1 is a schematic flow chart of iPI model-free adaptive global nonsingular fast terminal sliding-mode control method according to an embodiment of the present invention;
FIG. 2 is a schematic diagram illustrating the operation flow of iPI model-free adaptive global nonsingular fast terminal sliding-mode control method for a hypersonic aircraft aerodynamic thermal ground simulation system according to an embodiment of the present invention;
fig. 3(a) is a schematic diagram of a three-dimensional structure of a hypersonic velocity missile according to an iPI model-free adaptive global nonsingular fast terminal sliding mode control method according to an embodiment of the present invention;
FIG. 3(b) is a schematic two-dimensional dimension diagram of a hypersonic velocity missile according to an embodiment of the invention, in which iPI a model-free adaptive global nonsingular fast terminal sliding mode control method is adopted;
FIG. 4(a) is a schematic diagram illustrating a finite element simulation of aerodynamic heat of a hypersonic velocity missile according to an embodiment of the present invention in an iPI model-free adaptive global nonsingular fast terminal sliding mode control method;
FIG. 4(b) is a wall average temperature sampling schematic diagram of aerodynamic heat of a hypersonic velocity missile according to iPI model-free adaptive global nonsingular fast terminal sliding mode control method in an embodiment of the invention;
FIG. 4(c) is a schematic diagram illustrating data fitting of aerodynamic heat of a hypersonic velocity missile according to iPI a model-free adaptive global nonsingular fast terminal sliding mode control method according to an embodiment of the present invention;
FIG. 5 is a control framework diagram of iPI model-free adaptive global nonsingular fast terminal sliding-mode control method according to an embodiment of the present invention;
fig. 6 is an output temperature graph (a) and a local enlarged view (b) of an iPI model-free adaptive global nonsingular fast terminal sliding mode control method of a hypersonic aircraft aerodynamic hot ground simulation system under iPI model-free adaptive global nonsingular fast terminal sliding mode control method (1), iPI model-free adaptive global nonsingular fast terminal sliding mode control method (2), iPI control method (3) and a conventional PID method (4), according to an embodiment of the present invention;
fig. 7 is a tracking error curve (a) and a local enlarged view (b) of a pneumatic thermal ground simulation system of an iPI model-free adaptive global nonsingular fast terminal sliding mode control method of a hypersonic aircraft under a iPI model-free adaptive global nonsingular fast terminal sliding mode control method (1), a iPI model-free adaptive global terminal sliding mode control method (2), a iPI control method (3) and a conventional PID method (4), according to an embodiment of the present invention;
fig. 8 is an output temperature graph (b) and a partial enlarged view (c) of an iPI model-free adaptive global nonsingular fast terminal sliding mode control method under an external disturbance (a) of the model-free adaptive global nonsingular fast terminal sliding mode control method according to an embodiment of the present invention, in a iPI model-free adaptive global nonsingular fast terminal sliding mode control method (1), a iPI model-free adaptive global terminal sliding mode control method (2), a iPI control method (3), and a conventional PID method (4);
fig. 9 is a tracking error curve (a) and a local enlarged view (b) of an iPI model-free adaptive global nonsingular fast terminal sliding mode control method under disturbance of the model-free adaptive global nonsingular fast terminal sliding mode control method for aerodynamic hot ground simulation system of hypersonic aircraft according to an embodiment of the present invention under iPI model-free adaptive global nonsingular fast terminal sliding mode control method (1), iPI model-free adaptive global terminal sliding mode control method (2), iPI control method (3), and conventional PID method (4).
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, specific embodiments accompanied with figures are described in detail below, and it is apparent that the described embodiments are a part of the embodiments of the present invention, not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making creative efforts based on the embodiments of the present invention, shall fall within the protection scope of the present invention.
In the following description, numerous specific details are set forth in order to provide a thorough understanding of the present invention, but the present invention may be practiced in other ways than those specifically described and will be readily apparent to those of ordinary skill in the art without departing from the spirit of the present invention, and therefore the present invention is not limited to the specific embodiments disclosed below.
Furthermore, reference herein to "one embodiment" or "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one implementation of the invention. The appearances of the phrase "in one embodiment" in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments.
The present invention will be described in detail with reference to the drawings, wherein the cross-sectional views illustrating the structure of the device are not enlarged partially in general scale for convenience of illustration, and the drawings are only exemplary and should not be construed as limiting the scope of the present invention. In addition, the three-dimensional dimensions of length, width and depth should be included in the actual fabrication.
Meanwhile, in the description of the present invention, it should be noted that the terms "upper, lower, inner and outer" and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, and are only for convenience of describing the present invention and simplifying the description, but do not indicate or imply that the referred device or element must have a specific orientation, be constructed in a specific orientation and operate, and thus, cannot be construed as limiting the present invention. Furthermore, the terms first, second, or third are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
The terms "mounted, connected and connected" in the present invention are to be understood broadly, unless otherwise explicitly specified or limited, for example: can be fixedly connected, detachably connected or integrally connected; they may be mechanically, electrically, or directly connected, or indirectly connected through intervening media, or may be interconnected between two elements. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
Example 1
Referring to fig. 1 to 5, for a first embodiment of the present invention, an iPI model-free adaptive global nonsingular fast terminal sliding mode control method is provided, the method of the present invention is based on a super-local model of a hypersonic aircraft aerodynamic thermal ground simulation system model-free control, combines iPI, a nonlinear ESO observer, a global nonsingular fast terminal sliding mode surface, an equivalent control rate, and an adaptive approach law, and designs a controller u (t) to realize target tracking; referring to fig. 5, a model-free adaptive global nonsingular fast terminal sliding mode control block diagram of the hypersonic aircraft aerodynamic thermal ground simulation system iPI of the present invention specifically includes:
s1: according to the law of conservation of energy, a mathematical model of a hypersonic aircraft aerodynamic heat ground simulation system and a super-local model without model control are established. It should be noted that the hypersonic aircraft aerodynamic heating ground simulation system includes:
a non-contact radiant heater, an electric power regulating device and a calorimetric sensor;
establishing an input and output energy conservation equation according to the energy conservation law to obtain the current temperature T1And the conduction angle alpha of the triac, as follows,
wherein, the left side U of the equationIIs the input voltage, i.e. the voltage across the power supply, R is the sum of the resistances of the non-contact radiant heaters, alpha is the conduction angle of the triac, and to the right of the equation areThe heat energy output by internal energy consumed by the non-contact radiation heater, heat energy lost in the convection heat exchange process, heat energy lost in the heat conduction process and the heat radiation effect, c, m and T1、T0A, epsilon and delta t are respectively the specific heat capacity, mass, current temperature, initial temperature, surface area, blackness coefficient and working time of the non-contact radiation heater, beta, lambda, sigma and F are respectively convection heat transfer coefficient, heat conduction coefficient, Stefin-Boltzmann constant and angle coefficient;
when the controlled object model is a single-input single-output system, the controlled object model is converted into a super-local model without model control, as follows,
y(n)＝G+χu(t)
wherein, y(n)The method is expressed as an nth derivative of an output quantity y to time t, n is generally 1 or 2, u is expressed as an input quantity, G is expressed as a set of all unknown disturbances, the unknown disturbances include external disturbances and system internal nonlinear disturbances, and χ is expressed as a non-physical adjustable parameter.
S2: and carrying out unknown disturbance prediction on the hypersonic aircraft aerodynamic heat ground simulation system by using a nonlinear ESO observer. The steps to be explained are as follows:
according to a super-local model without model control, two sides of an input and output energy conservation equation are divided by delta t and terms are shifted to obtain a mathematical model of the pneumatic thermal ground simulation system of the hypersonic aircraft, as follows,
wherein the content of the first and second substances,
is T1The derivative with respect to the time at is,
alpha corresponds to y in the model-free controlled hyper-local model(n)U; sin2 alpha brings periodic vibration to the system and does not bring any vibration to the systemThe convergence of the whole has an effect, the term containing sin2 α can be considered as an input perturbation, A ε σ FT1 4Can be seen as a higher order output disturbance of the system and thus
The sum of all disturbances, which can be considered as both input and output disturbances, corresponds to G of the hyper-local model, which can be observed by an observer;
T1＝x3,G＝x4
wherein x is3Is the actual value T of the output1，x4In order to achieve a complete disturbance G,
is x3The first order differential of the first order of the,
is x4First order differential of (a) gamma is x4First order differentiation of;
unknown disturbance prediction is carried out on the pneumatic thermal ground simulation system of the hypersonic aircraft, a nonlinear ESO observer is established, and the following steps are carried out,
e1＝z1-x3,e2＝z2-x4
β1＞0,β2＞0
wherein Z is1Is x3Estimated value of, Z2Is x4Is determined by the estimated value of (c),
is Z1The first order differential of the first order of the,
is Z2First order differential of (1), beta1And beta1Is the gain of the parameter adjustment and the gain,
the tracking error expression defining the output is as follows,
e(t)＝y*-y
where e is the tracking error, y*Is an output target;
the model-free controller is obtained by closed-loop control based on the model-free controlled super-local model, as follows,
wherein the content of the first and second substances,
is an estimate of the value of G,
is y*Is the first order differential of (d), delta (e) is the iPI closed loop feedback control rate, delta (e) ═ Kpe(t)+Ki∫e(t)dt；
To attenuate the observed disturbances, an auxiliary controller u is added to the modeless controllerauxThe following, as follows,
wherein u isauxIs controlled according to a global nonsingular fast terminal sliding mode.
S3: based on the global nonsingular fast terminal sliding mode surface weakening approach buffeting, low convergence speed and singularity. It is also to be noted that, establishing a global nonsingular fast terminal sliding mode surface includes:
η＞0,ι＞0
wherein eta and iota are adjustable gains, p and q are positive odd numbers, the inequality p < q < 2p is satisfied, e (0) is an initial error, and s (0) ═ 0 solves the problem of approaching buffeting, and e (tau) + iota e (tau))p/qSolves the problems of slow convergence speed and singularity,
is the first differential of the slip form surface s;
establishing a tracking error e and an auxiliary controller uauxThe mathematical relationship between them, as follows,
wherein the content of the first and second substances,
in order to observe the error, the error is observed,
gidisturbing an upper bound for the observation error;
according to
Substituting the above formula into a global nonsingular fast terminal sliding mode surface, calculating to obtain an equivalent control rate, as follows,
according to sliding mode accessibility
The obtained approach rate was as follows,
wherein, k is the adjustable gain,
in order to adaptively perturb the upper bound adaptation rate,
s4: and defining an equivalent control rate and a self-adaptive approach law according to the sliding mode accessibility condition to obtain a sliding mode control rate and finish target tracking. What should be further described in this step is:
the iPI model-free self-adaptive global nonsingular rapid terminal sliding mode controller u (t) of the hypersonic aircraft aerodynamic thermal ground simulation system is obtained by simultaneously fusing an auxiliary controller, an equivalent controller and an approach rate, as follows,
wherein u isaux＝ueq+ucor；
Further, a Lyapunov function stability criterion expression is established, and the convergence of the model-free adaptive global nonsingular fast terminal sliding mode control method is verified iPI, and the method comprises the following steps:
wherein, satisfy
Referring to fig. 2, the work flow of the hypersonic aircraft aerodynamic heating ground simulation system mainly comprises the following steps:
(1) collecting aerodynamic thermal data of the hypersonic aircraft: carrying out finite element numerical simulation on the hypersonic missile through a given flight environment and a given wall material type number; and acquiring the average temperature of the wall surface of the missile at each moment, and performing linear fitting on the sampled data to obtain an expected output value, namely a target value, of the whole hypersonic aircraft pneumatic thermal ground simulation system so as to compare the expected output value with the output value of an actual controller.
(2) The hypersonic aircraft aerodynamic heating ground simulation control system comprises: designing a controller to control a quartz lamp heating system; the target value is loaded into the control board, the conduction angle alpha of the bidirectional thyristor is changed through the control board, the output voltage U is further changed, different output voltage U values correspond to different quartz lamp heating system electric powers P, the actual temperature T1 output by the quartz lamp heater is obtained through the sensor, the tracking error e is obtained through comparison with the target value, the actual temperature T1 is fed back to the controller through a closed loop to adjust the conduction angle alpha of the bidirectional thyristor, and finally tracking control is achieved.
(3) Ground simulation test feedback: and (3) carrying out a heating test on the test piece by using the quartz lamp heater, detecting the performance of the test piece, analyzing the feasibility of the material, selecting the material, and if the material cannot be replaced, carrying out the first step operation again, thereby optimizing the design of the thermal protection system.
Referring to fig. 3, the hypersonic missile is drawn by finite element simulation, and the specific parameters of the missile are as follows: the total length is 7600mm, the projectile body length is 4270mm, the projectile body diameter is 1168.4mm, the included angle of the guidance part is 7 degrees, the radius of the guidance head is 30mm, the included angle is 12.84 degrees, the flying environment is 32km, the speed is 6.0 Mach number, and the attack angle is 0 degree for cruising.
Referring to fig. 4, the simulation diagram, the wall surface average temperature sampling diagram and the average temperature curve fitting diagram of finite element simulation of the missile are shown, and the fitting curves are as follows:
y*＝1.848*10-5t8-0.001497t7+0.04917t6-0.8402t5
+7.977t4-41.34t3+93.82t2+151t+287.4
referring to fig. 5, which is a block diagram of model-free adaptive global nonsingular fast terminal sliding mode control of a hypersonic aircraft aerodynamic thermal ground simulation system iPI, and is a further description of the second step hypersonic aircraft aerodynamic thermal ground simulation control system of fig. 2, according to the schematic diagram of fig. 5, a controller u (t) is composed of 4 parts: 1. the self-adaptive global nonsingular fast terminal sliding mode surface provides an equivalent control rate and a self-adaptive approach law; 2. model-free control iPI closed loop feedback control rate; 3. first order differentiation of the desired target; 4. observing value of system unknown disturbance G by utilizing nonlinear ESO observer
Preferably, it should be further noted that, compared with the prior art, the embodiment discloses an iPI model-free adaptive global nonsingular fast terminal sliding mode control method, which aims to track an expected temperature within a limited time by adopting a iPI model-free adaptive global nonsingular fast terminal sliding mode control method, weaken buffeting in a control process, accelerate a convergence speed, and ensure a robust performance of the whole control process; the method comprises the following steps of (1) realizing system linearization by combining a super-local model in model-free control with a nonlinear ESO extended state observer; the problems of jitter, convergence stagnation, singularity control and the like in an approaching stage are solved by adopting a global nonsingular fast terminal sliding mode surface, an equivalent control rate and a self-adaptive approaching law.
Example 2
Referring to fig. 6 to 9, a second embodiment of the present invention is different from the first embodiment in that the test comparison verification of an iPI model-free adaptive global nonsingular fast terminal sliding mode control method is provided, and specifically includes:
in this embodiment, the output temperature and the tracking error of the hypersonic aircraft aerodynamic thermal ground simulation system are measured and compared in real time by adopting the hypersonic aircraft aerodynamic thermal ground simulation system under iPI model-free adaptive global nonsingular fast terminal sliding mode control method (1), iPI model-free adaptive global terminal sliding mode control method (2), iPI control method (3) and traditional PID method (4).
And (3) testing environment: referring to fig. 4(c), the hypersonic aircraft pneumatic thermal ground simulation system is operated on a simulation platform to simulate and track an expected target curve, and the hypersonic aircraft pneumatic thermal ground simulation system is respectively used for testing under iPI model-free self-adaptive global nonsingular fast terminal sliding mode control method (1), iPI model-free self-adaptive global terminal sliding mode control method (2), iPI control method (3) and traditional PID method (4) and obtaining test result data; in all the four methods, the automatic test equipment is started, MATLB software programming is used for realizing simulation test of the comparison method, simulation data are obtained according to test results, 4 groups of data are tested in each method, each group of data is sampled for 15s, each group of data is calculated to obtain input temperature and tracking error of each group of data, and the input temperature and the tracking error of each group of data are compared with expected target temperature input by simulation to calculate the error.
Referring to fig. 6, 7, 8 and 9, an output temperature curve graph and a partial enlarged graph, an error tracking curve comparison graph and a partial enlarged graph of a hypersonic aircraft aerodynamic hot ground simulation system under iPI model-free adaptive global nonsingular fast terminal sliding mode control method (1), iPI model-free adaptive global terminal sliding mode control method (2), iPI control method (3) and a traditional PID method (4), and an error tracking curve comparison graph and a partial enlarged graph under external disturbance are shown.
Referring to fig. 7(a), for external disturbances, the time varying resistance R is as follows:
R＝3.08×(1+0.0045y*)
iPI model-free adaptive global terminal sliding mode control method (2):
wherein the content of the first and second substances,
iPI control method (3):
the specific embodiment has the following parameter settings as shown in the following table:
table 1: and a parameter table of a hypersonic aircraft pneumatic thermal ground simulation system.
Table 2: iPI data sheet of model-free adaptive global nonsingular fast terminal sliding mode control method.
Table 3: iPI data sheet of model-free adaptive global terminal sliding mode control method.
Table 4: iPI and a PID data table.
Referring to fig. 6, it can be seen intuitively that the target curve can be tracked effectively by the 4 methods, and in fig. 6(b), when the time is 0-0.2 s, a large overshoot amount occurs in the method (3) and the method (4).
Referring to fig. 7, it can be seen that a certain steady-state error occurs in the early stage of the method (2), and buffeting is obvious; the rapidity and buffeting of the method (3) are relatively poor; the method (4) exhibits a large overshoot.
Referring to fig. 8, it can be seen intuitively that, in the case of external disturbance, 4 methods can generally track the target curve, and in fig. 8(c), when the time is 0-0.2 s, the target curve cannot be effectively tracked in the early stage of the method 3 and the method (4), and a large overshoot exists.
Referring to fig. 9, it can be seen intuitively that, under the condition of external disturbance, the control precision in the early stage of the method (2) is poor, and a certain error exists; the rapidity of the method (3) is poor, and the high-frequency switching amplitude in the later period is large; the overshoot of the method (4) is large and the rapidity is slow.
Referring to fig. 6 to 9, it can be analyzed that the control method of the present invention is superior to other 3 methods in 4 aspects of steady-state error, rapidity, overshoot, and control accuracy, and benefits from that the iPI model-free adaptive global nonsingular fast terminal sliding mode control method of the present invention weakens the buffeting phenomenon in the control process, accelerates the convergence rate, and ensures the robustness of the control overall process.
It should be noted that the above-mentioned embodiments are only for illustrating the technical solutions of the present invention and not for limiting, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, which should be covered by the claims of the present invention.
Claims (8)
1. An iPI model-free adaptive global nonsingular fast terminal sliding mode control method is characterized by comprising the following steps: comprises the steps of (a) preparing a mixture of a plurality of raw materials,
according to the law of conservation of energy, establishing a mathematical model of a hypersonic aircraft aerodynamic heat ground simulation system and a super-local model without model control;
carrying out unknown disturbance prediction on the hypersonic aircraft aerodynamic heat ground simulation system by using a nonlinear ESO observer;
based on the global nonsingular fast terminal sliding mode surface weakening approach buffeting, low convergence speed and singularity;
defining an equivalent control rate and a self-adaptive approach law according to the sliding mode accessibility condition to obtain a sliding mode control rate and finish target tracking;
the hypersonic aircraft pneumatic heat ground simulation system comprises a non-contact radiation heater, an electric power regulating device and a calorimetric sensor;
establishing an input and output energy conservation equation according to the energy conservation law to obtain the current temperature T1And the conduction angle alpha of the triac, as follows,
wherein, the left side U of the equationIThe input voltage is the voltage at two ends of the power supply, R is the sum of the resistances of the non-contact radiation heater, alpha is the conduction angle of the bidirectional thyristor, the right side of the equation is respectively used for the internal energy consumed by the non-contact radiation heater, the heat energy lost in the convection heat exchange process, the heat energy lost in the heat conduction process and the heat energy output by the heat radiation effect, and c, m, T1、T0A, epsilon and delta t are respectively the specific heat capacity, mass, current temperature, initial temperature, surface area, blackness coefficient and working time of the non-contact radiation heater, and beta, lambda, sigma and F are respectively the convection heat transfer coefficient, heat conduction coefficient, Stefin-Boltzmann constant and angle coefficient.
2. The iPI model-free adaptive global nonsingular fast terminal sliding-mode control method according to claim 1, wherein: comprises the steps of (a) preparing a mixture of a plurality of raw materials,
when the controlled object model is a single-input single-output system, the controlled object model is converted into the model-free control super-local model, as follows,
y(n)＝G+χu(t)
wherein, y(n)The method is expressed as nth derivative of an output quantity y to time t, n is generally 1 or 2, u (t) is expressed as an input quantity, G is expressed as a set of all unknown disturbances, the unknown disturbances include external disturbances and system internal nonlinear disturbances, and χ is expressed as a non-physical adjustable parameter.
3. The iPI model-free adaptive global nonsingular fast terminal sliding-mode control method according to claim 2, wherein: comprises the steps of (a) preparing a mixture of a plurality of raw materials,
according to the model-free control super-local model, dividing two sides of the input and output energy conservation equation by delta t and performing item shifting to obtain a mathematical model of the hypersonic aircraft aerodynamic heat ground simulation system, as follows,
wherein the content of the first and second substances,
is T1The derivative with respect to the time at is,
alpha respectively corresponds to y in the model-free controlled super-local model(n)U; while sin2 alpha brings periodic vibration to the system, and does not influence the convergence of the whole system, the term containing sin2 alpha is regarded as input disturbance, and A epsilon sigma FT1 4Seen as higher order output disturbances of the system and hence
The sum of all disturbances, which is considered to contain both input and output disturbances, corresponds to the G of the hyper-local model, which can be observed by an observer.
4. The iPI model-free adaptive global nonsingular fast terminal sliding-mode control method according to claim 3, wherein: also comprises the following steps of (1) preparing,
T1＝x3,G＝x4
wherein x is3Is the actual value T of the output1，x4In order to achieve a complete disturbance G,
is x3The first order differential of the first order of the,
is x4First order differential of (a) gamma is x4The first order differential of (1), χ is expressed as a tunable parameter in a non-physical sense;
and carrying out unknown disturbance prediction on the hypersonic aircraft aerodynamic heat ground simulation system, and establishing the nonlinear ESO observer, as follows,
e1＝z1-x3,e2＝z2-x4
β1>0,β2>0
wherein z is1Is x3Estimate of z2Is x4Is determined by the estimated value of (c),
is z1The first order differential of the first order of the,
is z2First order differential of (1), beta1And beta2Is the gain of the parameter adjustment and the gain,
5. the iPI model-free adaptive global nonsingular fast terminal sliding-mode control method according to claim 4, wherein: also comprises the following steps of (1) preparing,
the tracking error expression defining the output is as follows,
e(t)＝y*-y
where e is the tracking error, y*Is an output target;
obtaining a model-free controller through closed-loop control according to the model-free controlled super-local model, as follows,
wherein the content of the first and second substances,
is an estimate of the value of G,
is y*Is the first order differential of (d), delta (e) is the iPI closed loop feedback control rate, delta (e) ═ Kpe(t)+Ki∫e(t)dt；
In order to attenuate the observed disturbances, an auxiliary controller u is added to the modeless controllerauxThe following, as follows,
wherein u isauxIs controlled according to a global nonsingular fast terminal sliding mode.
6. The iPI model-free adaptive global nonsingular fast terminal sliding-mode control method according to claim 5, wherein: establishing the global nonsingular fast terminal sliding mode surface, including,
wherein eta, eta,
For adjustable gain, p and q are positive odd numbers, and satisfy inequality p<q<2p, e (0) as the initial error, s (0) ═ 0 solves the approach buffeting problem, e (τ) + iota e (τ)p/qSolves the problems of slow convergence speed and singularity,
is the first differential of the slip-form surface s.
7. The iPI model-free adaptive global nonsingular fast terminal sliding-mode control method according to claim 6, wherein: also comprises the following steps of (1) preparing,
establishing a tracking error e and an auxiliary controller uauxThe mathematical relationship between them, as follows,
wherein the content of the first and second substances,
in order to observe the error, the error is observed,
gifor observation error disturbance upper bound, G is the set of all unknown disturbances;
according to
Substituting the above formula into the global nonsingular fast terminal sliding mode surface, calculating to obtain an equivalent control rate,as follows below, the following description will be given,
according to sliding mode accessibility
The obtained approach rate was as follows,
wherein, k is the adjustable gain,
in order to adaptively perturb the upper bound adaptation rate,
8. the iPI model-free adaptive global nonsingular fast terminal sliding-mode control method according to claim 7, wherein: comprises the steps of (a) preparing a mixture of a plurality of raw materials,
simultaneously fusing the auxiliary controller, the equivalent controller and the approach rate to obtain an iPI model-free self-adaptive global nonsingular fast terminal sliding mode controller u (t) of the hypersonic aircraft aerodynamic heat ground simulation system, as follows,
wherein u isaux＝ueq+ucor。
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